The OP asks our advice because
.... I am a bit appalled by the idea to throw away an otherwise intact tent which wasn't used that much.
This is really a question of how far down the trail of leaving no trace you should feel obliged to go. Throwing away the tent leaves a trace; buying a new tent -- buying anything -- leaves a trace. But still, one can carry anything to absurdity, which would be the case in re-waterproofing this tent. (The OP does not mention cost as a factor.)
I have two suggestions. (1) Give the tent to someone with the warning that isit has no waterproofing. It may be fine for desert car-camping. (2) Spend time picking up litter from the roadside or some other environmental cleanup project, and/or contribute some money to an environmental fund. I am sure you can more than compensate for the discarding of the tent with your sweat and/or your checkbook.